Inner amenable groups having no stable action

Abstract

We construct inner amenable and ICC groups having no ergodic, free, probability-measure-preserving and stable action. This solves a problem posed by Jones-Schmidt in 1987.

7 pages

References in corpus (1)

• Stability in orbit equivalence for Baumslag-Solitar groups and Vaes groups

Cited by in corpus (6)

• Invariant means and the structure of inner amenable groups
• Stable actions of central extensions and relative property (T)
• Inner amenability, property Gamma, McDuff II_1 factors and stable equivalence relations
• Inner amenable groupoids and central sequences
• Stable actions and central extensions
• Groups with infinite FC-center have the Schmidt property